The Obama administration decided not to appoint World Bank President Robert Zoellick to a second five-year term as the bank chief Wednesday announced his June departure.

Mr. Zoellick, a U.S. citizen appointed by the White House under a Republican president, ran the Bretton Woods institution during one of the most volatile economic times in modern history.

Although technically, the bank’s global membership selects a new leader, Washington appoints its choice under the unwritten rules established since the U.S. helped to found the institution in the wake of the second World War.

The Obama administration hasn’t yet made public a decision on Mr. Zoellick’s successor, but Under Secretary Lael Brainard is heading the search committee. Ms. Brainard, former Treasury Secretary Lawrence Summers and Secretary of State Hilary Clinton are among the names mentioned in press reports as possible appointments.

During Mr. Zoellick’s tenure, the global political architecture has experienced a shift of unprecedented power toward emerging economies, a dynamic fueled by the 2008 financial crisis and Europe’s sovereign-debt woes. China, India and Brazil, for example, are now major drivers of global growth and have secured stronger political positions in the international arena, particularly through the creation of the Group of 20 industrialized and developing nations.

“The Bank has recognized that we live in a world of multiple poles of growth where traditional concepts of the ‘Third World’ are now outdated and where developing countries have a key role to play as growth drivers and responsible stakeholders,” Mr. Zoellick said in a statement.

“At the same time, we’ve scaled up our support to poor people, countries, and communities and shown that the bank can be an indispensable innovator, catalyst, and driver of a modernized multilateralism,” he said.

Mr. Zoellick presided over the first capital increase at the bank in more than two decades while it provided a record $247 billion for infrastructure projects, the private sector, agriculture, trade finance, education, health and social safety nets throughout the developing world.

The Obama administration also decided against another term for Republican appointee, John Lipsky, who last year stepped down as the deputy managing director of the International Monetary Fund. Instead, the White House appointed senior economic adviser David Lipton to the IMF’s no. 2 post.